Question

The electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle (as shown in figure) is $-Nql\hat{j}$. Determine the value of $N$.

Answer 1

Answer: 1.73

The given system of charges can be considered as two dipoles of charges ' $+q$ ' and ' $-q$ '. Let $p$ be the dipole moment of the dipole of charges $+q$ and $-q$ (placed at point $B$ ).
The horizontal components of $\vec{p}$ (due to charges at $A,B$ and $C$ ) cancel each other and vertical components add up.
So, the net dipole moment of system of charges,
${\vec{p}}_{nat}=2p\cos 30^{\circ }(-\hat{j})=2ql\left(\frac{\sqrt{3}}{2}\right)(-\hat{j})$
$=-\sqrt{3}ql\hat{j}$
$=-1.73ql\hat{j}$